Sharp Hardy's Inequalities in Hilbert Spaces Article Swipe

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Dimitar K. Dimitrov , I. Gadjev , Mourad E. H. Ismail ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2306.08172

We study the behavior of the smallest possible constants $d(a,b)$ and $d_n$ in Hardy's inequalities $$ \int_a^b\left(\frac{1}{x}\int_a^xf(t)dt\right)^2\,dx\leq d(a,b)\,\int_a^b [f(x)]^2 dx $$ and $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big)^2\leq d_n\,\sum_{k=1}^{n}a_k^2. $$ The exact constant $d(a,b)$ and the precise rate of convergence of $d_n$ are established and the extremal function and the ``almost extremal'' sequence are found.

Related Topics

Mathematics

Combinatorics

Hilbert Space

Mathematical Analysis

Concepts

Mathematics Combinatorics Hilbert space Function (biology) Sequence (biology) Hardy space Constant (computer programming) Mathematical analysis Chemistry Programming language Biochemistry Computer science Biology Evolutionary biology

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2306.08172
PDF: https://arxiv.org/pdf/2306.08172
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Cited By: 1
Related Works: 10
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DOI: https://doi.org/10.48550/arxiv.2306.08172

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Title: Sharp Hardy's Inequalities in Hilbert Spaces

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Language: en

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Publication year: 2023

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Publication date: 2023-06-13

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Authors: Dimitar K. Dimitrov, I. Gadjev, Mourad E. H. Ismail

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Landing page: https://arxiv.org/abs/2306.08172

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Concepts: Mathematics, Combinatorics, Hilbert space, Function (biology), Sequence (biology), Hardy space, Constant (computer programming), Mathematical analysis, Chemistry, Programming language, Biochemistry, Computer science, Biology, Evolutionary biology

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